2.9 KiB
| type | domain | description | confidence | source | created |
|---|---|---|---|---|---|
| claim | internet-finance | Doubly stochastic processes where arrival rate itself is random capture realistic uncertainty in demand forecasting | likely | Whitt et al., 'Staffing a Service System with Non-Poisson Non-Stationary Arrivals', Cambridge Core, 2016 | 2026-03-11 |
Cox processes model arrival rate uncertainty through stochastic intensity functions enabling capacity planning under forecast uncertainty
Cox processes (doubly stochastic Poisson processes) treat the arrival rate itself as a stochastic process rather than a deterministic function. This captures the realistic scenario where you don't know the exact arrival rate — you have a forecast with uncertainty. The arrival rate λ(t) becomes a random variable, and arrivals are Poisson conditional on the realized rate.
Whitt et al. extend their staffing framework to handle Cox processes, where the arrival rate itself is uncertain. This is more realistic than assuming you know the exact time-varying arrival rate. In practice, you have forecasts with error: "we expect 100-150 requests per hour" rather than "exactly 127 requests per hour."
The Cox process framework adds a second layer of randomness: first, the arrival rate is drawn from a distribution (capturing forecast uncertainty), then arrivals are Poisson given that rate (capturing arrival randomness). This doubly stochastic structure means the resulting arrival process is more variable than Poisson — it has peakedness > 1 even if the conditional arrivals are Poisson.
This matters for capacity planning because forecast uncertainty compounds arrival randomness. If you size capacity assuming you know the exact arrival rate, you'll be systematically under-provisioned when forecasts are uncertain. The Cox process framework quantifies how much additional safety capacity is needed to handle forecast error.
Evidence
- Whitt et al. (2016) extend square-root staffing to Cox processes where arrival rate λ(t) is itself a stochastic process
- Cox processes produce peakedness > 1 even when conditional arrivals are Poisson, because rate uncertainty adds variance
- The framework handles both time-varying rates (non-stationary) and rate uncertainty (stochastic intensity) simultaneously
Relevance to Pipeline Forecasting
Living Capital pipeline faces genuine forecast uncertainty: we can predict "futardio launch waves happen after major market moves" but not "exactly 23 launches will arrive Tuesday at 2pm." The arrival rate is itself uncertain. Cox process modeling would let us quantify: given historical forecast error, how much extra capacity do we need beyond the expected rate?
This is particularly relevant for burst detection: if we see arrival rates exceeding forecast confidence intervals, that's a signal to scale capacity aggressively rather than waiting for queue depth to grow.
Relevant Notes:
- domains/internet-finance/_map
Topics:
- core/mechanisms/_map